1. Field of the Invention
This invention relates in general to data processing, and more particularly to faster transforms that use early aborts and precision refinements.
2. Description of Related Art
Transforms, which take data from one domain (e.g., sampled data) to another (e.g., frequency space), are used in many signal and/or image processing applications. Such transforms are used for a variety of applications, including, but not limited to data analysis, feature identification and/or extraction, signal correlation, data compression, or data embedding. Many of these transforms require efficient implementation for real-time and/or fast execution where compression may or may not be used.
Data compression is desirable in many data handling processes, where too much data is present for practical applications using the data. Commonly, compression is used in communication links, to reduce transmission time or required bandwidth. Similarly, compression is preferred in image storage systems, including digital printers and copiers, where “pages” of a document to be printed may be stored temporarily in memory. Here the amount of media space on which the image data is stored can be substantially reduced with compression. Generally speaking, scanned images, i.e., electronic representations of hard copy documents, are often large, and thus make desirable candidates for compression.
In data processing, data is typically represented as a sampled discrete function. The discrete representation is either made deterministically or statistically. In a deterministic representation, the point properties of the data are considered, whereas, in a statistical representation, the average properties of the data are specified. In particular examples referred to herein, the terms images and image processing will be used. However, those skilled in the art will recognize that the present invention is not meant to be limited to processing images but is applicable to processing different data, such as audio data, scientific data, image data, etc.
In a digital image processing system, digital image signals are formed by first dividing a two-dimensional image into a grid. Each picture element, or pixel, in the grid has associated therewith a number of visual characteristics, such as brightness and color. These characteristics are converted into numeric form. The digital image signal is then formed by assembling the numbers associated with each pixel in the image into a sequence which can be interpreted by a receiver of the digital image signal.
Signal and image processing frequently require converting the input data into transform coefficients for the purposes of analysis. Often only a quantized version of the coefficients is needed (e.g. JPEG/MPEG data compression or audio/voice compression). Many such applications need to be done fast in real time such as the generation of JPEG data for high speed printers.
Pressure is on the data signal processing industry to find the fastest method by which to most effectively and quickly perform the digital signal processing. As in the field of compression generally, research is highly active and competitive in the field of fast transform implementation. Researchers have made a wide variety of attempts to exploit the strengths of the hardware intended to implement the transforms by exploiting properties found in the transform and inverse transform.
One such technique is the ISO 10918-1 JPEG International Standard/ITU-T Recommendation T.81. The draft JPEG standard is reproduced in Pennebaker and Mitchell, JPEG: Still Image Data Compression Standard, New York, Van Nostrand Reinhold, 1993, incorporated herein by reference. One compression method defined in the JPEG standard, as well as other emerging compression standards, is discrete cosine transform (DCT) coding. Images compressed using DCT coding are decompressed using an inverse transform known as the inverse DCT (IDCT). An excellent general reference on DCTs is Rao and Yip, Discrete Cosine Transform, New York, Academic Press, 1990, incorporated herein by reference. It will be assumed that those of ordinary skill in this art are familiar with the contents of the above-referenced books.
It is readily apparent that if still images present storage problems for computer users and others, motion picture storage problems are far more severe, because full-motion video may require up to 60 images for each second of displayed motion pictures. Therefore, motion picture compression techniques have been the subject of yet further development and standardization activity. Two important standards are ISO 11172 MPEG International Standard and ITU-T Recommendation H.261. Both of these standards rely in part on DCT coding and IDCT decoding.
However, research generally focuses on specific techniques, such as the above-mentioned techniques that used DCT coding to provide the desired degree of compression. Nevertheless, other transforms may be used to provide certain advantages under certain circumstances. For example, in the DCT compression coding method discussed above, an input image is divided into many uniform blocks and the two-dimensional cosine transform function is applied to each block to transform the data samples into a set of transform coefficients to remove the spatial redundancy. However, even though a high compression rate may be attained, a blocking effect, which may be subtle or obvious, is generated. Further, vector quantization methods that may be utilized by the compression system are advantageous due to their contribution to the high compression rate. On the other hand, a sub-band method may reduce the blocking effect which occurs during high rates of data compression. The wavelet transform (WT) or Sub-Band Coding (SBC) methods encode signals based on, for example, time and frequency components. As such, these transform methods can be useful for analyzing non-stationary signals and have the advantage that they may be designed to take into account the characteristics of the human visual system (HVS) for image analysis.
Scaled terms may be used to replace multiplicative constants like cosine terms in a Discrete Cosine Transform (DCT) with a minimum number of additions/subtractions. However, the scaled terms merely approximate the constants in the transform equations. Thus, some error is accepted to keep the precision confined to a fixed number of bits or to minimize the number of operations. If the resulting numbers are further from a decision boundary (e.g., a threshold value or a quantization boundary) than the maximum possible error, the result will not be affected by the approximations. However, the resulting numbers may be determined, during the incremental calculations, to require additional precision. Yet, the original input values are no longer available in the registers, and refetching the original input values from memory can impose cycles associated with cache misses and memory latency. The brute-force option is to perform an inverse transform (e.g., an IDCT) on the values, and then re-run the forward transform (e.g., FDCT, sometimes denoted just DCT) with higher precision. The disadvantage of the brute force approach is that operations are wasted.
It can be seen then that there is a need to provide faster transforms that use early aborts and precision refinements to save processing cycles thereby providing faster transform calculations and decreased execution times.